APPLICATION OF STATISTICAL PROCESS CONTROL IN

List of TablesLIST OF TABLESTable 4.1An example of SPC plan template for Type 3 slider body . 44Table 4.2Reorganized SPC plan template for Type 3 slider body . 45Table 4.3An example of proposed SPC plan . 46xiii

Chapter 1 IntroductionCHAPTER 1 INTRODUCTION1.1BackgroundWith the increasing demand by customers for high quality and low cost products in theglobal market, the need for quality improvement has become increasingly important in allindustries in recent years.In order to supply defect-free products to customers and to reduce the cost on defectiveparts in production, Statistical Process Control (SPC) techniques have been widely usedfor quality assurance. SPC originated when Shewhart control charts, such as Average andRange charts, were invented by W. A. Shewhart at Western Electric during the 1920’s. InAverage and Range chart, sample means are plotted on the Average chart to detect theshift of process mean, while sample range or standard deviations are plotted on the Rangeor Standard Deviation chart, respectively, to detect the shift of process variation. In lateryears, Individual and Moving range chart, Cumulative Sum chart, ExponentiallyWeighted Moving Average chart are developed to monitor process in different situations.Control chart, as the main tool in SPC was proven to be very effective in many industries.Histogram, Check Sheet, Pareto Chart, Cause and Effect Diagram, Defect ConcentrationDiagram, and Scatter Diagram are combined with Control Chart to serve as the“Magnificent Seven” powerful tools to effectively locate problem and find causes. Theymade SPC very useful in improving the performance of the process and the quality of theproducts.Most of the successful applications of SPC are for mass productions. The nature of multiproduct and short-run of injection mould manufacturing will further create challenging1

Chapter 1 Introductionproblems for the mould maker to maintain high quality through the application of SPC.Hence it is important to develop an effective approach in the manufacture of injectionmoulds in this research.1.2Problem StatementsMany definitions such as “low volume”, “short-run” or “small batch” can be found in theliteratures to describe a production process in which the batch size or lot size is mall,usually less than 50 units. This kind of production process presents challenging problemsin the application of SPC.The main problem associated with low volume production is due to lack of sufficient datato properly estimate process parameters, i.e. process mean and variance, the meaningfulcontrol limits for control charts are hard to attain. The availability of rationalhomogeneous subgroups is the basic assumption of traditional SPC. In low-volumeproduction, this kind of homogeneous subgroup does not exist. To solve it, short-run SPCmethods are proposed.Firstly, the important basis of short-run SPC is to focus on the process, not the parts. Ifthe process is in control and capable, quality of the parts manufactured by it will beguaranteed. To improve the performance of the process, the various parts manufacturedby it are taken for analysis. To solve the contradiction between variations of parts anddemand of sample number, the concept of forming part family, which results inincreasing the number of samples, was proposed. A part family means family of products“that are made by the same process that have common traits such as the same material,configuration, or type of control characteristic”. (Griffth, 1989) To form a part family, itmust meet two requirements: homogeneous variance and equal mean (Koons and Luner,2

Chapter 1 Introduction1991, Evans and Hubele 1993). The equal mean here means the mean of coded data ortransformed data, which is usually the difference between the measured value andnominal value on one particular quality characteristic. Under the assumptions ofhomogeneous variance and equal mean, quality characteristics with different nominalvalues but similar process variations can be plotted on the same control chart using thecoded data. Process parameters and control limits are calculated based on these codeddata collected from different part types. But most of research works focused on the shortrun productions, in which a certain number of part types are alternatively produced.An injection mould is a mechanical tool in which molten plastic is injected at highpressure to produce plastic products. Figure 1.1 shows the injection moulding process ofplastic product. An injection mould allows the manufacturers to mass-produce of theplastic parts that are highly identical in terms of dimension and appearance. For eachplastic product, one single cavity mould, a multi-cavity mould or several identical mouldsmay be needed. For each new plastic product design, a new mould has to be made.Therefore, the manufacture of injection mould is characterized as one-off.A mould assembly usually consists of mould base, cavity insert, core insert, otheraccessories and standard components. Figure 1.2 shows an example of an injection mouldassembly. Slider or lifter is needed if there is an undercut in the plastic part. Tomanufacture the part, a series of machining processes are needed.3

Chapter 1 IntroductionFigure1.1 Injection moulding process of plastic productCavitySliderassemblyCoreMould baseLifterassemblyFigure 1.2 An injection mould assembly (Alam, 2001)4

Chapter 1 IntroductionDue to the high diversity of plastic products, the shapes, dimensions, and features ofmould parts can be very different one from another. The manufacturing processes of themould parts can also be very diverse in terms of process type, machine type, machinesetting, cutting tool, workpiece holding and fixturing, and cutting conditions. Theproblem of high variation of parts and high variation of manufacturing processes makesthe application of SPC in the manufacture of injection mould more challenging comparedwith other short-run production systems.1.3Research ObjectivesThe application of short-run SPC in the manufacture of injection mould consists of twomain parts – SPC planning and SPC implementation. SPC planning involves defining andidentifying SPC processes, forming and identifying part families, selecting datatransformation methods, and selecting control charts. SPC implementation involvescollecting data, transforming data, plotting transformed data on control charts, analyzingand interpreting the charts and suggesting possible causes for out-of-control situations.As SPC implementation in the manufacture of mould is similar to other those used inmanufacturing industries, which have been studied by other researchers, SPC planning isthus the main part of this research.The main objective of this research is to develop a framework consisting of methods andprocedures on SPC application in the manufacture of injection mould.The second objective is to analyze, summarize and generalize the characteristics ofdifferent mould parts and the different machining features on the parts and themanufacturing processes of the mould parts.5

Chapter 1 IntroductionThe third objective is to propose an approach to define and identify a suitable SPCprocess. The part family is formed and identified based on the characteristics of themould parts manufacturing to make the application of control charts both statisticallymeaningful and operable.6

Chapter 2 Literature ReviewCHAPTER 2 LITERATURE REVIEW2.1 Traditional Statistical Process ControlStatistical Process Control (SPC) is a systematic set of tools to solve process-relatedproblems. Through the application of SPC tools, possible reasons that cause a process tobe out of control can be identified and corrective actions can be suggested. A controlchart is the primary tool of SPC and basically used to monitor the process characteristics,e.g., the process mean and process variability (Duncan, 1988, Montgomery, 2001).The most common types of variable control charts include:(1)Average and Range (X and R) Charts(2)Average and Standard Deviation (X bar and S) Charts(3)Individual and Moving Range (X and MR) ChartsCollectively, above charts are usually called Shewhart charts, as they are based on thetheory developed by Dr. Walter A. Shewhart. As Shewhart charts are relativelyinsensitive to small shifts in the process, two effective charts may be used to supplementthem when there are small shifts in the process.(1)Cumulative Sum Control (Cusum) Chart(2)Exponentially Weighted Moving Average (EWMA) Control ChartAs they are effective in detecting small shifts, but not as effective as Shewhart charts indetecting large shifts, an approach of using a combined Cusum-Shewhart or EWMAShewhart is proposed. Simply adding the Shewhart chart to Cusum chart or EWMA chartcan effectively improve the responsiveness to both large and small shifts (Montgomery,2001).7

Chapter 2 Literature ReviewThe control charts in traditional SPC are designed to monitor a single product with largeproduction runs. The availability of rational homogeneous subgroups is the basicassumption of traditional SPC. Many researchers proposed that 20-25 samples withsample size of 4-5 from a single part type should be used to calculate the meaningfulcontrol limits (Duncan, 1986, Griffith, 1996, Montgomery, 2001). Therefore, at least 80125 units are needed for setting up a control chart. Since low-volume production does nothave the aforementioned type of homogeneous subgroups, short-run SPC methods havebeen proposed.2.2 Short-run Statistical Process ControlA short-run problem can be characterized in several ways, but the problem essentiallyconcerns insufficient data or untimely data for the determination of control limits.Usually it belongs to the following general categories:1. Not having enough parts in a single production run to achieve or maintain controllimits of the process;2. The process cycles are too short that even large-size production runs are overbefore data can be gathered;3. Many different parts are made for many different customers (in small-lot sizes)To apply SPC to any of the above situations, the main emphasis is not on the parts, but onthe process. Parts are the media to convey the information of the process performance,and the main concern is the process.Short-run SPC methods work on a variety of different parts, each with a differentnominal value for the concerned quality characteristic. To make the control chart8

Chapter 2 Literature Reviewstatistically meaningful, appropriate data transformation and part family formation areneeded (Griffith, 1996).2.2.1 Data transformation methodsSeveral data transformation methods have been proposed in the literature by Bothe(1988), Cullen (1989), Evans (1993), and Crichton (1988) respectively. The mostrepresentative ones are discussed below:2.2.1.1 Bothe’s approachThe most commonly used and the simplest data transformation method, Deviation-fromnominal, was first proposed by Bothe (1988). It uses the deviation between the measuredand nominal values as the individual data point. This method can be used for bothIndividual Chart and Average and Range Charts. This method is used for processvariability that is approximately the same for all part types (Al-salti et al, 1992).2.2.1.2 Bothe and Cullen’s approachSubsequently, Bothe and Cullen proposed another data transformation method, thatdivides the value of the deviation from nominal by the range of the part type (Bothe et al.,1989). This method can also be used in both Individual Chart and Average and RangeChart.For Individual Chart, the plot point isX A nominalX plotpoint (2.1)RAwhere XA is the measured value of one part of type A, and RA is the historical averageBBBBrange of part type A. It can be calculated using equation in below:9

Chapter 2 Literature Reviewm RRA Ajj 1m(2.2)where RAj is the range of the jth historical subgroup of part type A. m is the number ofBBBBhistorical subgroups of part type A.For Average and Range charts, the plot points are:XA XARAX plotpoint Rplotpoint(2.3)RA (2.4)RAwhere XA is the average of measured value of part type A. It can be calculated using theBBequation in below:nXA XAii 1n(2.5)where XAi is the ith measured value of part type A. n is the number of measurements.BBBBX A is the mean of XA. It can be calculated using the equation in below:BBm XXA Ajj 1m(2.6)10

Chapter 2 Literature Reviewwhere X Aj is the jth subgroup of part type A. m is the number of subgroups of part typeBBA.RA is the historical average range of part type A. R A can be calculated using equationBBBB2.2.This method is used when the variation of the process differs significantly with differentpart types.2.2.1.3 Evans and Hubele’s approachIn this method, similar to Bothe and Cullen’s approach, the value of deviation fromnominal is divided by the tolerance of the part type A (Evans et al., 1993).For Individual Chart, the plot point isX plot po int X A nominalTA(2.7)where XA is the measured value of one part of type A, and TA is the tolerance of part typeBBBBA.For Average and Range Charts, the plot points are:X plotpoint Rplotpoint XA XA2TA(2.8)RA2TA(2.9)11

Chapter 2 Literature Reviewwhere XA is the average of measured value of part type A. It can be calculated usingBBequation 2.5. X A is the mean of XA. It can be calculated using equation 2.6. TA is theBBBBtolerance of part type A.This method is used when the tolerance of different part types are significantly differentand the process variation also differs with the different tolerances.2.2.1.4 Crichton’s approachIn this approach, the deviation from nominal is divided by the nominal value (Crichton,1988).For Individual chart, the plot point isX A nominalnominalX plotpoint (2.10)where XA is the measured value of one part of type A.BBFor Average and Range chart, the plot points are:XA XAX plotpoint Rplotpoint(2.11)XARA (2.12)XAwhere XA is the average of measured value of part type A. It can be calculated usingBBequation 2.5. X A is the mean of XA. It can be calculated using equation 2.6.BBThis method is used when process variability differs significantly from one part toanother and also increases with the nominal size.12

Chapter 2 Literature Review2.2.2 Part family formationFor simple short-run productions, parts are manufactured with constant process parametersetting, but variation in size. Parts made by the same process naturally belong to the samepart family. Only data transformation is needed to apply traditional control charts to theshort-run productions. But in modern manufacturing practices, situations are always notso simple. Parts made by the same process may be very different from one to another inmaterial or geometrical characteristics. As a result, the corresponding process parametersettings may be different. In these complicated situations, after data transformation, thereare still four types of variation that exists in the transformed data produced by a particularprocess, as shown in Figure 2.1.Variation Type I refers to the variation caused by the differences between parts, such asdifference in material or in geometrical characteristics.Variation Type II refers to the variation caused by the different process parametersettings.Variation Type III refers to the variation caused by the shift of the process.Variation Type IV refers to the inherent process variation, which can be reduced byimproving process capability.The purpose of SPC is to eliminate type III variation, and to reduce type IV variation. Astatistically meaningful control chart is supposed to present only variation type III andtype IV. Therefore, variation type I and type II should be separated from variation typeIII and type IV in the control chart.13

Chapter 2 Literature ReviewTo remove the effect of variation type I and type II, the part family has to be carefullyformed to isolate these two types of variation, so that they will not co-exist within onepart family. Koons and Luner (1991) and Evans and Hubele (1993) both considered theeffect of type II variation. In their approaches, these two types of variation are removedby forming suitable part families.Inherent Variationof ProcessType IVA combination ofparameter settingsB combination ofparameter settingsVariationType IC combination ofparameter settingsVariationType IIVariationI II III IVD combination ofparameter settingsE combination ofparameter settingsShift of theProcessType IIIFigure 2.1 Types of variation existing in short-run productions.Koons and Luner’s approachAs the operating factors of a process might systematically affect the process performance,it is proposed that process performance would be monitored separately for eachcombination of the potentially significant factors. If subsequent analysis fails to show that14

Chapter 2 Literature Reviewthe operating factor has significant effect, it would be taken as a single process regardlessof the setting of that factor.In Koons and Luner’s approach (1991), it was done in a way that is characterized by“division”. Initially, it is assumed that all data set is produced from a single process. Thevalidity of this assumption is tested by statistical analysis. The predeterminedcharacteristic of each part is measured and recorded. Prior to the test, the data set istransformed by using Deviation from Nominal, which is subtracting the nominal valuefrom the measured value. The variance of each subgroup is used as a measure ofsubgroup variability. The subgroup variances are displayed in a Variance (S2) Chart. ThePPlimits of the variance chart are calcula

Statistical Process Control has been widely and successfully applied in many industries since it originated when Shewhart first proposed the concept of control chart in the 1920’s. As the traditional application of SPC demands a huge amount of data, the application of SPC in the short-run